# Problem 11
# In the 2020 grid below, four numbers along a diagonal line have been marked in red.

# 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
# 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
# 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
# 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
# 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
# 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
# 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
# 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
# 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
# 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
# 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
# 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
# 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
# 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
# 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
# 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
# 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
# 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
# 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
# 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

# The product of these numbers is 26*63*78*14 = 1788696.
# What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20*20 grid?

import unittest

def getSubMatrix(M, M_order, S_y, S_x, S_order):
    if S_x + S_order > M_order or S_y + S_order > M_order:
        return None
    S = [[0]*S_order for i in range(S_order)]
    for y in range(0, S_order):
        for x in range(0, S_order):
            S[y][x] = M[S_y + y][S_x + x]
    return S
    
    
def getGreatestProductOfMatrix(M, M_order):
    greatest = 1
    product = 1
    # horizontal
    for y in range(0, M_order):
        product = 1
        for x in range(0, M_order):
            product *= M[y][x]
        if product > greatest:
            greatest = product
    # vertical
    for x in range(0, M_order):
        product = 1
        for y in range(0, M_order):
            product *= M[y][x]
        if product > greatest:
            greatest = product
    # diagonal
    product = 1
    for x in range(0, M_order):
        product *= M[x][x]
    if product > greatest:
        greatest = product
    product = 1
    for x in range(0, M_order):
        product *= M[M_order - x - 1][x]
    if product > greatest:
        greatest = product
    return greatest;


def findGreatestProductAdjacentNumbers(M, M_order, n):
    greatest = 1
    for y in range(0, M_order):
        for x in range(0, M_order):
            S = getSubMatrix(M, M_order, y, x, n);
            if S == None:
                break
            product = getGreatestProductOfMatrix(S, n);
            if product > greatest:
                greatest = product 
    return greatest    
    
    
    
    
class TestP011(unittest.TestCase):
    def testGetSubMatrix(self):
        order = 3;
        M = [[0]*order for i in range(order)]
        M[0][0] = 0;  M[0][1] = 1;  M[0][2] = 2
        M[1][0] = 3;  M[1][1] = 4;  M[1][2] = 5
        M[2][0] = 6;  M[2][1] = 7;  M[2][2] = 8

        S = [[0]*1 for i in range(1)]
        S[0][0] = 0;
        self.assertEqual(S, getSubMatrix(M, order, 0, 0, 1))
        
        S[0][0] = 8;
        self.assertEqual(S, getSubMatrix(M, order, 2, 2, 1))
        
        self.assertEqual(None, getSubMatrix(M, order, 3, 0, 1))
        self.assertEqual(None, getSubMatrix(M, order, 0, 3, 1))
        
        S = [[0]*2 for i in range(2)]
        S[0][0] = 0; S[0][1] = 1;
        S[1][0] = 3; S[1][1] = 4;
        self.assertEqual(S, getSubMatrix(M, order, 0, 0, 2))
        
        S[0][0] = 4; S[0][1] = 5;
        S[1][0] = 7; S[1][1] = 8;
        self.assertEqual(S, getSubMatrix(M, order, 1, 1, 2))
        
        S[0][0] = 1; S[0][1] = 2;
        S[1][0] = 4; S[1][1] = 5;
        self.assertEqual(S, getSubMatrix(M, order, 0, 1, 2))
        
        S[0][0] = 3; S[0][1] = 4;
        S[1][0] = 6; S[1][1] = 7;
        self.assertEqual(S, getSubMatrix(M, order, 1, 0, 2))
        
        self.assertEqual(None, getSubMatrix(M, order, 2, 0, 2))
        self.assertEqual(None, getSubMatrix(M, order, 0, 2, 2))
        
    def testGetGreatestProductOfMatrix(self):
        M = [[0]*2 for i in range(2)]
        M[0][0] = 1; M[0][1] = 2;
        M[1][0] = 3; M[1][1] = 4;
        self.assertEqual(1, getGreatestProductOfMatrix(M, 1))
        self.assertEqual(12, getGreatestProductOfMatrix(M, 2))
        M[0][0] = 4; M[0][1] = 2;
        M[1][0] = 3; M[1][1] = 1;
        self.assertEqual(12, getGreatestProductOfMatrix(M, 2))
        M[0][0] = 4; M[0][1] = 2;
        M[1][0] = 1; M[1][1] = 3;
        self.assertEqual(12, getGreatestProductOfMatrix(M, 2))
        M[0][0] = 1; M[0][1] = 3;
        M[1][0] = 4; M[1][1] = 2;
        self.assertEqual(12, getGreatestProductOfMatrix(M, 2))
        
    def testFindGreatestProductAdjacentNumbers_2x2(self):
        M = [[0]*2 for i in range(2)]
        M[0][0] = 4; M[0][1] = 2;
        M[1][0] = 3; M[1][1] = 1;
        self.assertEqual(4, findGreatestProductAdjacentNumbers(M, 1, 1))
        self.assertEqual(4, findGreatestProductAdjacentNumbers(M, 2, 1))
        self.assertEqual(12, findGreatestProductAdjacentNumbers(M, 2, 2))
    
    def testFindGreatestProductAdjacentNumbers_3x3(self):
        M = [[0]*3 for i in range(3)]
        M[0][0] = 0;  M[0][1] = 1;  M[0][2] = 2
        M[1][0] = 3;  M[1][1] = 4;  M[1][2] = 5
        M[2][0] = 6;  M[2][1] = 7;  M[2][2] = 8
        self.assertEqual(7*8, findGreatestProductAdjacentNumbers(M, 3, 2))
        
        M[0][0] = 100;  M[0][1] = 1;  M[0][2] = 2
        M[1][0] = 3;  M[1][1] = 4;  M[1][2] = 5
        M[2][0] = 6;  M[2][1] = 7;  M[2][2] = 8
        self.assertEqual(100*4, findGreatestProductAdjacentNumbers(M, 3, 2))
        
        M[0][0] = 0;  M[0][1] = 1;  M[0][2] = 2
        M[1][0] = 3;  M[1][1] = 40;  M[1][2] = 5
        M[2][0] = 6;  M[2][1] = 70;  M[2][2] = 8
        self.assertEqual(40*70, findGreatestProductAdjacentNumbers(M, 3, 2))
        
if __name__ == '__main__':
    P011 = unittest.TestLoader().loadTestsFromTestCase(TestP011)
    unittest.TextTestRunner(verbosity=2).run(P011)
    M = [ 
            [ 8, 02, 22, 97, 38, 15,  0, 40, 00, 75,  4,  5,  7, 78, 52, 12, 50, 77, 91,  8],
            [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48,  4, 56, 62,  0],
            [81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 03, 49, 13, 36, 65],
            [52, 70, 95, 23,  4, 60, 11, 42, 69, 24, 68, 56,  1, 32, 56, 71, 37,  2, 36, 91],
            [22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
            [24, 47, 32, 60, 99,  3, 45,  2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],
            [32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70],
            [67, 26, 20, 68, 02, 62, 12, 20, 95, 63, 94, 39, 63,  8, 40, 91, 66, 49, 94, 21],
            [24, 55, 58,  5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
            [21, 36, 23,  9, 75,  0, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95],
            [78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 03, 80,  4, 62, 16, 14,  9, 53, 56, 92],
            [16, 39,  5, 42, 96, 35, 31, 47, 55, 58, 88, 24,  0, 17, 54, 24, 36, 29, 85, 57],
            [86, 56,  0, 48, 35, 71, 89, 07, 05, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
            [19, 80, 81, 68, 05, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77,  4, 89, 55, 40],
            [ 4, 52,  8, 83, 97, 35, 99, 16,  7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
            [88, 36, 68, 87, 57, 62, 20, 72, 03, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
            [04, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18,  8, 46, 29, 32, 40, 62, 76, 36],
            [20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74,  4, 36, 16],
            [20, 73, 35, 29, 78, 31, 90, 01, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 05, 54],
            [ 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 01, 89, 19, 67, 48]
        ]
    print "the greatest product of four adjacent numbers in any direction [%d]" % findGreatestProductAdjacentNumbers(M, 20, 4)